 # Q.4 (15 points) Determine the CRITICAL numbers of the function: f{x...

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Q.4 (15 points) Determine the CRITICAL numbers of the function: f{x)=x²(3x²+x-21). - Find f'(x) = Solve f'(x)=0,for x Also for each of the critical numbers determined above, use sign of second derivative to identify RELATIVE EXTREMA points of the function. [ Hint : evaluate values of second derivative for each of the critical numbers and conclude] f"(x)= Check signs of f"(c). Q.5 (5+5 points) Determine account balance at end of 7¹/² years if \$25000 is invested at 15% annual interest rate compounded monthly. Determine amount (in \$) that a person needs to invest now, if the person wishes to have \$ 25000 at end of 16 years, when invested at 35% annual interest rate compounded quarterly. Q.6 (5+4+4points) Determine critical numbers and all relative maximum/minimum points of the function : f(x) = 5+4x+9/x Domain : {1-00,0),(0,00)} - - - - - - Also evaluate ABSOLUTE Maximum Value of above over the interval [1,9] Q.7 (6 points) Evaluate each of the following values (correct to 3 decimal places) : f(-1), where f(x) = 2+2.3X+1.5 f( - 2.5), where f(x) = x² + In (3.5 - x)2 + 4

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